the rope will generate heat through the slings. Just imagine how quickly you pull it down. Do that through your bare hand at the same angle and speed and see how it feels. It gets hot. You would have to inch the rope along, take maybe 10 min. to slowly pull it to really leave no heat exchange to the nylon. A link or 'booty carabiner can be left instead if you prefer.

Plus the next climber to rap on it may not notice the wear or expect it to have been used that way..thus leaving a dangerous rappel anchor that looks brand new but has suffered some damage possibly unseen to the next party to use it.

If you are bailing from some unconventional spot (because of weather, getting too late, can't finish the climb, etc.), I wouldn't leave a rap ring, especially if it is alpine.

I assume anyone doing a route and then rappelling off of a non-conventional place will check the anchor and reinforce it if necessary. I've seen anchors on alpine routes that are falling apart just from being in the sun for years.

I disagree with leaving a rap ring "just in case" the next party might get hurt by rapping off your bail anchor. After all, they could easily get hurt even if you leave a rap ring... rodents chew through anchors, sun weakens webbing, etc. And what if you need to make 5 raps to get off of a route? Are you really going to leave/carry 5 rap rings or bail 'biners?

However, if you are rapping from a conventional, established rap spot, I would use rap rings, since it is likely that others will make the same rap in the future, and it is nice if not every single party has to re-establish the anchor every single time. (That being said, it is still the rappelling party's responsibility to check the integrity of the anchor)

As was mentioned, pulling your rope through webbing will damage the webbing.

Not only that, but depending on the logistics of the rappel the rope can damage the webbing while you and your partners are actually on rappel. Having done a bunch of climbing & canyoneering I've been able to closely observe how the rope behaves on the rap anchor while people are rapping down and the rope often moves back and forth through the anchor during their decent - usually not alot of movement, but enough to weaken webbing if that's what you're rapping off (it takes surprising little friction and movement on a weighted rope running through webbing to actually damage the webbing).

There are many factors which come into play, but I prefer to minimize those factors and potential risks and throw a rap ring on the webbing.

Have I rapped solely off webbing before - yes. I wouldn't do it again unless there were no other options. I routinely have a rap ring and some webbing in my 'kit' when I'm climbing for those unforseen circumstances.